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Numerical solutions of the Schrödinger equation with source terms or time-dependent potentials
1Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
We present a new numerical method for the time-dependent Schrödinger equation with source terms and time-dependent potentials. This approach achieves high precision, comparable to standard methods, and allows for error estimation.
Area of Science:
- Quantum mechanics
- Computational physics
- Numerical analysis
Background:
- Solving the time-dependent Schrödinger equation is crucial for understanding quantum systems.
- Existing numerical methods face challenges with source terms and time-dependent potentials.
Purpose of the Study:
- To develop a precise numerical approach for the time-dependent Schrödinger equation.
- To handle equations with source terms and time-dependent potentials effectively.
Main Methods:
- Generalized Crank-Nicolson method.
- Euler-MacLaurin expansion for time-integrated nonhomogeneous terms.
Main Results:
- Numerical precision comparable to the generalized Crank-Nicolson method for homogeneous equations.
- The method accurately solves equations with source terms and time-dependent potentials.
- Systematic increase in precision allows for error estimation.
Conclusions:
- The developed approach offers a robust and accurate solution for complex quantum dynamics.
- This method enhances the reliability of numerical simulations in quantum mechanics.
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